Convergence of synchronous and asynchronous algorithms in multiclass networks

The Nash equilibrium point for optimum flow control in a noncooperative multiclass environment is studied. Convergence properties of asynchronous as well as synchronous algorithms are investigated. The convergence of a greedy algorithm for the n users case is proved, and necessary and sufficient conditions for the convergence of asynchronous algorithms are obtained. Since asynchronous algorithms do not converge for all values of the weighting factors, one must be careful in their choice. An introduction to the literature and an extension of a not very widely known theorem for the convergence of Gauss-Seidel algorithms in the linear systems theory are given